Cobb is not dreaming

I recently watched Inception for the second time, and I managed to convince myself that Cobb is not dreaming.

Here is a statistically sound way (albeit not very cost-effective) of finding out whether I am in a dream or not. We know for a fact that the map of a dream in finite, made to look infinite. All I have to do is find the end of the map. So, I drive to a random airport and take a plane to a random location. If I ever get there, I take another plane and fly to a second random location, and then a third, and so on. The more random locations I visit the more improbable it becomes that I am in a dream. Why? Because it is statistically improbable that the architect of the dream would have simulated so many random locations on the globe.

In the movie, Cobb travels from Japan, to France, to Kenya, to the United States. All along, he uses trains, helicopters and cars to travel long distances inside very complex cities. Additionally, he is the one that decides to go to France and Kenya specifically. Nobody suggested that to him. Hence, these locations are somewhat random. What are the chances that an architect had simulated such a complex environment in great detail in advance? Thus, with very high probability, Cobb is NOT dreaming.